Evolving Dark Energy with $w\ne -1$

Theories of evolving quintessence are constructed that generically lead to deviations from the $w=-1$ prediction of nonevolving dark energy. The small mass scale that governs evolution, $m_{\varphi }\approx {10}^{-33}\mathrm{eV}$, is radiatively stable, and the “Why now?” problem is solved. These results rest on seesaw cosmology: Fundamental physics and cosmology can be broadly understood from only two mass scales, the weak scale $v$ and the Planck scale $M$. Requiring a scale of dark energy ${\rho }_{\mathrm{DE}}^{1/4}$ governed by $v^2/M$ and a radiatively stable evolution rate $m_{\varphi }$ given by $v^4/M^3$ leads to a distinctive form for the equation of state $w(z)$. Dark energy resides in the potential of a hidden axion field that is generated by a new QCD-like force that gets strong at the scale $\Lambda \approx v^2/M\approx {\rho }_{\mathrm{DE}}^{1/4}$. The evolution rate is given by a second seesaw that leads to the axion mass $m_{\varphi }\approx {\Lambda }^2/f$, with $f\approx M$.

Figure 1

Contours for $w$ and $w^{\prime }$.

Figure 2

$w(z)$ for four choices of ($f/M_{\mathrm{Pl}}$, ${\varphi }_0/f$). The solid lines are ${\varphi }_0/f=0.6\pi$ while the dashed lines have ${\varphi }_0/f=0.7\pi$. The lines are labeled by their value of $f/M_{\mathrm{Pl}}$.